DefinitionDefinition: Literature-sourcedProof: Not applicableaudited 2026-08-31

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

Word reversal and language reversal

Definition

Let $w : n \to Σ$ be a word over an alphabet $Σ$ . Its reversal is the word $w^{R} : n \to Σ$ defined by $w^{R} (i) : = w (n - 1 - i) (i < n) .$ Equivalently, if $w = a_{0} a_{1} \dots a_{n - 1}$ , then $w^{R} = a_{n - 1} a_{n - 2} \dots a_{0}$ . In particular, $ε^{R} = ε$ .

If $L \subseteq Σ^{*}$ is a language, its reversal is $L^{R} : = {w^{R} : w \in L} .$

Remarks

Reversal changes the order of letters but not the alphabet or the word length.
The definition is pointwise on words first and only then lifted to languages.

Depends on

Used by

Nothing in the library uses this result yet.

Dependency tree · two levels

6 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

Jean Gallier and Jocelyn Quaintance, Introduction to the Theory of Computation: Some Notes for CIS511 (standard reference, not scraped)